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This book covers two essential PDE-based image processing fields: image denoising and image inpainting. It describes the state-of-the-art PDE-based image restoration and interpolation (inpainting) techniques, focusing on the latest advances in PDE-based image processing and analysis, and explores novel techniques involving diffusion-based models and variational schemes. The PDE and variational schemes clearly outperform the conventional approaches in these areas, and can successfully remove image noise and reconstruct missing or highly degraded regions, while preserving the essential features and avoiding unintended effects. The book addresses researchers and graduate students, but is also well suited for professionals in both the mathematics and electrical engineering domains, as it provides rigorous mathematical investigations of the image processing models described, as well as mathematical treatments for the numerical approximation schemes of these differential models.
"This concise, well-written monograph presents state-of-the art of nonlinear PDE-based filtering methods and image impainting techniques. ... The book can be recommended to students and scientists working in the area of mathematics, computer science and electrical engineering. The readers of the book should have a basic knowledge in PDEs, numerical analysis and digital image processing." (Wieslaw Kotarski, zbMath 1411.94001, 2019)